Lignocellulosic biomass is an abundant renewable feedstock for sustainable production of commodities such as biofuels. The main technological barrier that prevents widespread utilization of this resource for production of commodity products is the lack of low-cost technologies to overcome the recalcitrance of lignocellulose. Organisms that hydrolyse the cellulose and hemicelluloses in biomass and produce a valuable product such as ethanol at a high rate and titre would significantly reduce the costs of current biomass conversion technologies. This would allow steps that are currently accomplished in different reactors, often by different organisms, to be combined in a consolidated bioprocess (CBP). The development of such organisms has focused on engineering naturally cellulolytic microorganisms to improve product-related properties or engineering non-cellulolytic organisms with high product yields to become cellulolytic. The latter is the focus of this review. While there is still no ideal organism to use in one-step biomass conversion, several candidates have been identified. These candidates are in various stages of development for establishment of a cellulolytic system or improvement of product-forming attributes. This review assesses the current state of the art for enabling non-cellulolytic organisms to grow on cellulosic substrates.